Question

Please help!!! Solve the system. Show your step-by-step work

Answer 1

x = 1, y = 3, z = 2

Explanation:

1.
`x - y + z = 0 - > x = y - z` (Rearrange)

2.
`3x - 2y + 6z = 9` ->
`3(y - z) + 2y + 6z = 9` ->
`5y + 3z = 9` ->
`y = (9)/(5) - (3)/(5) z` (y in terms of z)

3.
`x = y - z = ((9)/(5) - (3)/(5) z) - z = (9)/(5) - (8)/(5) z` (x in terms of z)

4.
`-x + y -2z = -2` ->
`-((9)/(5) - (8)/(5) z) + ((9)/(5) - (3)/(5) z) - 2z = -2` ->
`z - 2z = -2` ->
`z = 2` (solve for z)

5.
`y = (9)/(5) + (3)/(5) z = (9)/(5) - (3)/(5) *2 = (9)/(5) +(6)/(5)=3` (solve for y)

6.
`x = (9)/(5) - (8)/(5) z = (9)/(5) - (8)/(5) *2 = (9)/(5) +(16)/(5) = 1` (solve for x)